Orthogonal expansion of Gaussian wind velocity field and PDEM-based vibration analysis of wind-excited structures

An effective procedure for simulation of random wind velocity field by the orthogonal expansion method is proposed in this paper. The procedure starts with decomposing the fluctuating wind velocity field into a product of a stochastic process and a random field, which represent the time property and the spatial correlation property of wind velocity fluctuations, respectively. By an innovative orthogonal expansion technology, the stochastic process for wind velocity fluctuations may be represented as a finite sum of deterministic time functions with corresponding uncorrelated random coefficients. Similarly, the random field can be expressed as a combination form with only a few random variables by the Karhunen-Loeve decomposition. This approach actually simulates the wind velocity field with stochastic functions other than methods such as spectral representation and proper orthogonal decomposition. In the second part of the paper, the probability density evolution method (PDEM) is employed to predict the stochastic dynamic response of structures subjected to wind excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic responses of structures. The solution of this equation will give rise to instantaneous probability density function of the responses. Finally, the accuracy and effectiveness of the approach in representing the random wind velocity field and PDEM-based dynamic response of wind-excited building are investigated.     

路面谱激励下的运营桥梁结构的响应分析

基于运营桥梁结构中不同路谱激励样本的差异,分别计算了特定样本下,车速变化时桥梁结构、运营车辆的位移、速度、加速响应。采用标准路面等级的功率谱密度,运用余弦叠加方法,模拟了不同样本的各等级路面谱激励;采用直接积分的方法,计算了加入路面随机激励后的车桥振动的微分方程,分析了不同路面等级、不同车速下系统的响应。结果表明：随机相位角、功率谱密度等级分别影响路面谱激励的样本形状和幅值大小,不同随机样本具备相同统计特征;对于系统的响应曲线,路面平整度等级对幅值影响相对显著,车速变化对形状影响相对显著;根据算例中不同路面平整度等级的计算结果,给出了相应的工程建议。     

基于反应谱的土与结构相互作用体系演变随机激励响应

利用功率谱与反应谱的转换关系,建立了演变随机过程输入功率谱密度函数表达式,提出了分析土与结构相互作用体系演变随机过程的反应谱分析方法,该方法利用新规范中的加速度反应谱作为目标谱,计算与之相对的功率谱并按该功率谱作为地震输入谱进行土与结构相互作用体系随机地震反应分析.研究表明,该方法反映了地震动和相互作用体系的动力特性,是进行土与结构相互作用体系随机地震反应分析的一种有效方法.     

Reliability-based vector nonstationary random critical earthquake excitations for parametrically excited systems

The study considers the earthquake response of stack-like structures subjected to simultaneous action of random horizontal and vertical earthquake acceleration components. The governing equation of motion in this case is approximated by a set of coupled randomly time varying ordinary differential equations. The components of earthquake accelerations are modelled as nonstationary Gaussian random processes that are obtained by multiplying deterministic modulating functions with partially specified stationary random processes. Specifically, it is assumed that the matrix of power spectral density (psd) functions of the stationary components is not known, while, the variance, average rate of zero crossings, entropy rate and frequency range of interest are taken to be known. The unknown input psd matrix is determined such that the reliability index associated with a specified structure performance function is minimized. The solution procedure employed, combines the theory of Hasofer–Lind reliability indices, response surface modelling and constrained nonlinear optimization tools. The critical input psd matrix so obtained leads to the definition of excitation models that produce the least favorable response, which, at the same time, possess a few of the well known properties of earthquake loads. A numerical example that illustrates the concepts developed with reference to a chimney structure is provided.     

Nonlinear response and reliability analysis of tunnels under strong earthquakes

The damages of tunnels under earthquakes showed that soil–rock deposits around a tunnel have significant effects on its response to earthquake excitations, caused by the spatial variability and correlation of the soil properties, which may properly be modelled as a random field. This paper studied these effects through modelling the surrounding soil as a random field on the response of a tunnel and made some comparisons with the corresponding deterministic analysis. A two-dimensional finite element model of the tunnel-soil system was examined, and the corresponding random field was simulated by the spectral representation method. The results revealed that the corners of the tunnel are the critical locations for the axial force and bending moment. The comparisons showed that the results of the deterministic analysis usually yield higher results than the corresponding random field results. The reliabilities of a tunnel for two limit-state functions were considered: one is defined as exceeding the design limit according to the Chinese design code, whereas the other is exceeding the ultimate strength of the reinforced concrete tunnel lining. The equivalent extreme events were formulated for the respective limit-state functions, from which the tunnel system reliability can be evaluated. The probability density evolution method was used to calculate the stochastic response and reliability of the tunnel under a strong earthquake.     

谐波合成法在动力荷载模拟中的应用

详细介绍了利用谐波合成法模拟随机过程的思路。根据模拟点数的不同,将谐波合成法分为单点模型和考虑相关性的多点模型,以桥面不平度和桥面纵向脉动风速的模拟为例,说明了谐波合成法在工程中的应用。通过对模拟结果的功率谱与目标功率谱密度的比较,验证了谐波合成法的可靠性和准确性。     

利用带主坐标缩阶技术的SPT模拟随机时间序列

结合CPT产生缩阶的主坐标功率谱矩阵,利用SPT对主坐标功率谱矩阵进行了分解模拟主坐标时间序列,进而模拟随机时间序列,从而大幅压缩了计算时间,并对精度没有太大影响,该方法具有较好的实用性和可操作性。     

Active control of tall buildings against stochastic wind forces

This paper presents the design of active control forces for tall buildings subjected to stochastic wind forces, in order to suppress the vibrations in the building. From the available data on wind speeds, the spectral density function of the wind forces can be evaluated. A filter is designed to simulate the spectrum of the wind forces in order to design the stochastic control forces. A numerical example is given for the active control of a tall building against stochastic wind, using an active tendon mechanism. The possibility of completely suppressing the vibrations in the building using this approach is demonstrated.     

高层多塔连体结构连廊随机地震反应分析

在多点激励地震反应分析中,传统的随机振动分析方法存在数值积分耗时太长的问题。为了克服这一缺点,ANSYS通过对输入功率谱采用对数形式的分段线性表示,然后采用解析解积分方式进行随机振动求解,计算效率精确高效。采用该方法对一高位隔震多塔连体结构进行双向水平地震动作用下多点激励随机地震响应分析,并对空间变化地震动作用下连廊桁架杆件内力响应极大值的均值进行比较分析。分析结果表明:在水平双向地震动作用下,考虑行波效应和部分相干效应会使连廊杆件轴力有所增大,在设计时应引起重视。     

成层场地由基岩反应谱直接计算地表反应谱的等效线性化方法

以太平洋地震工程中心NGA强震数据库为基础，同时收集并分析处理了2008年汶川地震和2011年日本太平洋冲地震的强震记录。通过对近4000个水平地震记录的分析，获得了水平地震动峰值速度(PGV)与阻尼比5%的最大拟速度谱值的简便统计关系式，并与已有研究进行对比验证了该公式的适用性。为了将该公式应用到场地地震反应分析中，用该关系式对近场强震记录进行了回归分析并验证了其适用性。对于水平成层场地，利用笔者提出的PGV与最大拟速度谱的关系式以及速度与应变的近似关系，可由该层的反应谱计算其等效应变，从而可按照等效线性化方法的原理求得传递函数。以加速度反应谱与功率谱密度函数之间的相互转换关系为基础，以功率谱为载体，假定输入地震动为平稳随机过程，根据随机振动理论可由传递函数和输入功率谱算得各层的反应谱。对实际工程场地和竖向钻孔场地的分析表明，该方法有较好的计算精度和适用性。     

潮间带原位剪切波速特性探讨及应用分析

探讨适用于近海及潮间带场区的剪切波速原位测试方法,针对黄海小洋口潮间带,进行剪切波速的原位测试,分析剪切波速的变化规律及其与土体参数的统计关系,并建立复合关系进行剪切波速预测分析,同时基于剪切波速测试成果进行应用分析。研究结果如下：通过经适性对比,近海及潮间带剪切波速测试采用单孔悬挂式方法较为适宜;剪切波速与测点深度呈相关性较好幂函数关系,按土层的统计关系分析,幂函数及其误差包络线基本反映了规律性;与土体物理力学参数的统计关系呈相关性较好幂函数或线性关系;基于测试资料,建立剪切波速 、孔隙比e、密度 及有效自重应力 的复合关系,通过计算对比分析,按此方法可以取得良好的剪切波速预测结果,亦可进行相关指标的预测分析;通过原位测试资料,进行场地土类划分对比、动参数规律性分析及地震液化判定分析,可为工程勘测、设计人员提供参考。     

扩张卡尔曼滤波器有限元法耦合算法及其隧道工程应用

本文用随机过程和最优估计理论分析隧道围岩随开挖的非确定性动态，将卡尔曼滤波器的滤波修正---不断产生新息量功能与有限元法的迭代计算、场域分析功能进行耦合，建立了能反映围岩动态非线性随机过程的耦合算法模型，并开发出具有可操作性的算法程序（ＥＫＦＦＥＭ）。本文以现场量测值为观测量的集合，以初始地应力和弹性模量等为过程状态量，对隧道围岩历时动态进行非确定性计算分析，揭示了围岩动态过程具有随机性的本质，进而为工程设计与施工提供依据     

空间相关多点地震动合成研究

在前人研究的基础上给出了一种合成考虑空间相关性多点地震动时程的方法,该方法通过对互功率谱密度矩阵简化,只需要对迟滞相干函数矩阵分解,不需要对互功率谱矩阵进行Cholesky分解,避免了算数矩阵运算,提高了合成的效率。用该方法编制了相应的程序,给出了合成的算例。     

相对运动法与绝对位移直接求解法算法误差分析

多点激励地震响应分析过程中,相对运动法和绝对位移直接求解法分别假定阻尼与内部节点相对速度、绝对速度成比例,由于阻尼假定的不一致,计算结果可能存在误差.采用随机振动分析方法对瑞利阻尼模型下2种求解方法计算结果之间的误差进行了理论分析,得出了2种算法下结构动态响应功率谱密度误差主要受激励频率与结构基频的比值、结构阻尼比影响...     

人群跳跃荷载的互功率谱模型

将人群跳跃荷载视为联合平稳随机过程,提出相干函数并结合已有的自功率模型,构建跳跃频率一致和不一致两种典型情况下的互功率谱模型。利用三维动作捕捉技术克服了人群跳跃荷载试验中同步测试的难题,并验证结果与测力板方法的一致性。由试验数据获得人群跳跃频率的分布和相干函数参数的取值。利用所提出的互功率谱模型,由随机振动理论计算结构加速度响应的自功率谱和均方根值。理论预测结果与已建大跨楼盖的实测响应结果对比表明,所建议的互功率谱模型和计算方法合理,可用于人群跳跃荷载作用下结构响应的计算与分析。     

单点和多点荷载输入的虚拟激励法实用求解模式

在实际工程中采用虚拟激励法（pseudo excitation method,PEM）往往需要编写复杂计算程序,为方便工程应用,建立了一种对应单点和多点荷载输入的虚拟激励法实用求解模式。考虑地震作用、风荷载等多种随机荷载,提取单点和多点荷载输入下计算结构虚拟响应的实用求解模式,并利用常规有限元分析软件的谐振稳态分析完成PEM核心计算,最后通过线性组合重新构建结构虚拟响应和功率谱密度函数的求解公式,从而在常规有限元分析软件中实现了PEM算法。由于采用建议方法可将PEM算法的核心计算交由有限元分析软件完成,在保持PEM高效准确计算优势的前提下显著提高了工作效率,避免了编写复杂计算程序,方便实际工程应用。通过两个典型数值算例验证了建议方法的正确性与有效性,并且指出其对于多种荷载工况的计算效率具有一定优势。     

Spectral characteristics of nonstationary random processes—response of a simple oscillator

This article analyzes the approaches to defining “spectral characteristics” derived from the spectral functions of nonstationary random processes. The processes considered are those for which an evolutionary power spectrum as designated by Priestley can be defined. Two basic approaches to defining spectral characteristics are reviewed. The first, characterized as geometric, leads to Vanmarke's spectral moments, which have proven to be very useful characteristics for stationary processes. However, these moments may be infinite for nonstationary processes, which creates problems for applications. The second approach, viewed as nongeometric, is based on Di Paola's pre-envelope covariances. The advantages and deficiencies of both approaches are discussed. It is also shown that the nongeometric spectral characteristics can be directly defined from the frequency domain as integrals of the one-sided auto- and cross-spectra of the evolutionary process and its derivatives. These nongeometric spectral characteristics are then used in defining parameters that characterize the central frequency and the bandwidth of evolutionary processes. To this end, the probability distributions of the process envelope are analyzed. It is demonstrated that suitable central frequencies and bandwidth factors can be defined from the probability density functions of the derivatives of the envelope and the phase.     

Generalized hermite analysis of nonlinear stochastic systems

By means of a generalized Hermite analysis we investigate nonlinear oscillator systems driven by white noise excitations. Nonstationary solutions of associated Fokker-Planck equations can be expanded by orthonormal polynomials which are generated if the Gaussian weighting function of the classical Hermite polynomials is replaced by stationary density distributions of the diffusion equation. In particular, this method is applied to calculate correlation functions and power spectra for the stochastic Duffing oscillator and for nondifferentiable restoring forces with backlash.     

Coupled stability analysis of thin-walled composite beams with closed cross-section

For the coupled stability analysis of thin-walled composite beam with closed cross-section subjected to various forces such as eccentric constant axial force, end moments, and linearly varying axial force, the efficient numerical method to evaluate the element stiffness matrix is newly presented based on the homogeneous form of simultaneous ordinary differential equations. The general bifurcation type of buckling theory for thin-walled composite box beam is developed based on the energy functional corresponding to semitangential rotations and semitangential moments. The coupled stability equations including variable coefficients and the force–displacement relationships are derived from the energy principle and explicit expressions for displacement functions are presented based on power series expansions of displacement components. The element stiffness matrix is evaluated by applying member force–displacement relationships to these displacement functions. In addition, the finite element model based on the cubic Hermitian interpolation polynomial is presented. In order to verify the accuracy and validity of this study, numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the available results from other researchers. Particularly, the influence of the eccentricity and the force ratio of axial forces, the fiber orientation, and the boundary conditions on the buckling behavior of composite box beam are parametrically investigated. Also the emphasis is given in showing the phenomenon of buckling mode change.     

二维任意裂隙网络裂隙–孔隙渗流模型的两种解法

 与裂隙网络渗流模型相比,裂隙–孔隙渗流模型(双重介质渗流模型)假定裂隙及裂隙切割而成的岩块均透水。这样可以只考虑较大裂隙形成的裂隙网络,而岩块及其内部的较小随机裂隙均作为连续孔隙介质进行渗流分析,从而减少裂隙网络中的裂隙数量以增加计算容量。讨论裂隙–孔隙渗流模型研究存在的问题,归纳剖析2种解法,即整体求解法与流量交换法。整体求解法中,裂隙作为有一定宽度的介质并划分为实体计算单元,与岩块单元的单元渗透矩阵合并成总体渗透矩阵进行求解。裂隙实体单元无需在网格划分时划出,只需在计算程序中对裂隙节点进行扩展。流量交换法中,裂隙系统和岩块系统分别形成渗透矩阵和渗流方程组,分别计算2个系统的渗流,2个系统之间通过流量交换,最终实现流量平衡和同一节点的水头一致,并指出水交换量只修正下游节点的渗流平衡方程。通过算例,比较2种解法的特点。还提出任意封闭回路在不增加节点前提下的三角形划分法。